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Alex Krüger 🇦🇷 @Crypto_Macro
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1/ A thread on the shape of the Futures curve: understanding Contango & Backwardation in all asset classes (Commodities, Equities, Fixed Income, Volatility, Foreign Exchange, Bitcoin).

--- long enough for an article, but writing articles is more time consuming than a tweetstorm.
2/ The price of Futures or Forwards can be expressed as a function of the Spot price and the cost of carry. This is mainly known as Interest Rate Parity. Some refer to it as the Cost of Carry Model. Futures and Forwards are in this case interchangeable words.
3/ Cost of Carry:

F = (S+s) e^{(r-c)t}

F = fwd price
S = spot price
s = storage cost
e = natural log base
r = risk-free interest rate (funding to finance the purchase of the fwd)
c = convenience yield or risk premium
t = time to delivery of forward…
4/ Rationale

An investor borrows at "r" to buy today an asset at price "S". It then immediately sells and agrees to deliver the asset in the future at price "F". Holding the asset will cost "s" in storage, and generate a return of "c", which counters the cost of funding "r".
5/ Arbitrage

IF price "F" would be greater than price "S" after accounting for storage and the difference between funding cost "r" and returns for holding "c", THEN the investor can borrow at "r", buy at "S", sell at "F", and make risk-free money, today.…
6/ Inneficient markets

In an inefficient market with few market participants, arbitrage opportunities will be plenty. The more the market grows, the more market participants will arbitrage these inefficiencies, until eventually becoming very small.
7/ Efficient markets

Market participants who perform arbitrage are arbitrageurs. In efficient markets it is their permanent trading activity that maintains inefficiencies reduced. By buying the cheap asset they make its price go up, and viceversa for the expensive.
8/ Equation Explanations

Convenience yield:

- For commodities, represents readily access (affected by crises)
- For equities, represents dividends
- For bonds, represents coupons

Storage cost: applicable to commodities (think warehousing, etc).…
9/ Variables contributing to Contango

. Higher rates (caused by e.g. Fed hikes, financial crises)
. Higher storage costs (caused by e.g. higher inventories, insurance)
. Lower convenience yield (caused by e.g. lack of political crisis for comms, lower dividends for equities).
10/ Variables contributing to Backwardation

. Lower rates
. Lower storage costs
. Higher convenience yield (e.g. for oil a political crisis in the Middle East would result in higher convenience yields)
11/ Contango

When the shape of the Futures Curve is upwards sloping => Futures are priced higher than spot => Fi > ... > F2 > F1 > S.

This is called Contango. It basically means that the cost of carry is positive.
12/ Backwardation

When the shape of the Futures Curve is downwards sloping => Futures are priced lower than spot => Fi < ... < F2 < F1 < S.

This is called Backwardation It basically means that the cost of carry is negative.
13/ Equities example

For equities backwardation takes place when interest rates are lower than dividend yields, which is usually driven by dovish monetary policy => the lower the rate the lower the cost of carry and the more backwardation. Simple math. Logical as well.
14/ Crude Oil example

When there is excessive inventory prices go into contango. Thus contango is associated with bear markets. Similarly, when there are inventory shortages or supply crises, prices go into backwardation. Thus backwardation is associated by bull markets.
15-1/ Other Commodities

- Natural Gas: very expensive to store => usually more in contango than oil.
- Agro: the commodities usually most in contango due to high risk premium caused by high volatility in producers hedging needs.
15-2/ Other Commodities

- Metals: usually high inventories => contango, but only slightly, as
storage is cheap and abundant (cost doesn't rise as much with inventory).
- Energy: non-storable (infinite storage costs) => no link between futures
& spot => better for forecasting.
16/ Volatility example

Volatility futures are often used for hedging portfolio equity exposure, and are usually in contango, as people places a higher risk premium in risks further out in time. When a panic strikes short term volatility spikes and futures go into backwardation.
17/ Futures prices as forecasts

Futures prices are linked to Spot prices via storage costs, interest rates & risk premiums. Hence Futures do not represent a forecast. When such link is weak, as with Energy, then futures are good for forecasting.…
18/ Normal Backwardation

Keynes theorized that for commodities backwardation was normal as producers looking to pre-sell a product would normally be willing to receive less for their product. Hence the term "Normal Backwardation".…
19/ Covered Interest Rate Parity (CIRP)

Cost of Carry Equation is equivalent to CIRP.

F = S (1 + rf) / (1 + rb)

F = fwd price
S = spot price
rf = reference currency
rb = base currency

FX is quoted in pairs as in AUDJPY:

AUD = base
JPY = reference…
20/ Cost of Carry vs Covered Interest Rate Parity

Just as in the Cost of Carry Model the arbitrageur borrows at "r" to buy at "S", in CIRP the arbitrageur borrows at "rf" to buy at "S".

These two are mathematically almost identical (easy to corroborate on excel).
21-1/ Carry Trade


- high yielding AUD, low yielding JPY
- carry trade = buy AUD & sell JPY
- trader receives AUD rates, pays JPY rates
- gets paid rates differential (the carry)
21-2/ Carry Trade

- if AUDJPY flat or up by fwd expiry, made money
- if AUDJPY down by less than the Carry, made money
- if AUDJPY down by more than the Carry, lost money
22-1/ Carry Trade Unwind

Forwards are marked to market. Those entering into AUDJPY carry trade on margin can be liquidated if AUDJPY drops. For pairs with significant carry trade this can generate significant unwinds, which accelerate a downmove, generating more unwinds.
22-2/ Carry Trade Unwind

Unwinds are related to stock market crashes, as those getting funding in lower rates such as the JPY's do not just invest in AUD but in any kind of risky asset. Risk positions are mostly correlated and move in tandem.…
23/ Emerging Markets Currencies example

EM currencies are usually high yielding relative to the USD, as EM countries have structurally higher inflation. EM currencies are generally quoted as USD/EM e.g. USDMXN. Thus the forwards (when quoted as USD/EM) are usually in contango.
24-1/ Bitcoin example

In a bull market, there is higher demand to borrow USD to buy bitcoin on margin => USD rates go up => contango

In a bear market, there is higher demand to borrow BTC to sell bitcoin on margin => BTC rates go up => backwardation.
24-2/ Bitcoin example

Bitcoin has no central bank => rates fully determined by market. Rates are usually relatively low due to its restrictive (deflationary) monetary policy. Furthermore BTC has historically been on a bull market, and thus in contango
24-3/ Bitcoin

Alternative interpretation of BTC contango: given aggressive bull, longs must pay shorts interest to entice them to short against the trend.

Contango represents an implied coupon payment for futures shorts i.e. short future, buy spot, hold until expiry = $$$.
24-4/ Bitcoin example

Bitcoin futures trade below spot (go into backwardation) in anticipation of forks. This article covers that well:…
25/ Summary of different asset classes

Commodities in contango => bearish
Volatility in contango => bullish for equities
FX, Bonds & Equities in contango => neither bullish nor bearish
Bitcoin in contango => bullish
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